Question: Multiply the following complex numbers: $({-5i}) \cdot ({5-i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5i}) \cdot ({5-i}) = $ $ ({0} \cdot {5}) + ({0} \cdot {-1}i) + ({-5}i \cdot {5}) + ({-5}i \cdot {-1}i) $ Then simplify the terms: $ (0) + (0i) + (-25i) + (5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 - 25)i + 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 - 25)i - 5 $ The result is simplified: $ (0 - 5) + (-25i) = -5-25i $